Searches for sterile neutrinos at the DANSS experiment

. DANSS is a highly segmented 1 m 3 plastic scintillator detector. The DANSS detector is placed under an industrial 3.1 GW th reactor of the Kalinin Nuclear Power Plant 350 km NW from Moscow. The distance to the core is varied on-line from 10.7 m to 12.7 m. The reactor building provides about 50m water-equivalent shielding against the cosmic background. DANSS detects almost 5000 ν e per day at the closest position with the cosmic background less than 3%. The inverse beta decay process is used to detect ν e . Sterile neutrinos are searched for assuming the 4 ν model (3 active and 1 sterile ν ). The exclusion area in the (cid:2) m 214 , sin 2 2 θ 14 plane is obtained using a ratio of positron energy spectra collected at different distances. Therefore results do not depend on the shape and normalization of the reactor ν e spectrum nor the detector efﬁciency. Results are based on 966 thousand antineutrino events collected at three different distances from the reactor core. The excluded area covers a wide range of the sterile neutrino parameters down to sin 2 2 θ 14 < 0 . 01 in the most sensitive region.

The survival probability of a reactor ν e at short distances in the 4ν mixing scenario (3 active and 1 sterile neutrino) is described by an effective expression 1 − sin 2 2θ 14 sin 2 1.27 m 2 14 [eV 2 ]L[m] E ν [MeV] .
The existence of sterile neutrinos would manifest itself in distortions of the ν e energy spectrum at short distances. At longer distances these distortions are smeared out and the rate is reduced by a factor of 1 − sin 2 (2θ 14 )/2. Measurements at only one distance from a reactor core are not sufficient since the theoretical description of the ν e energy distribution is considered not to be reliable enough. The most reliable way to observe such distortions is to measure the ν e spectrum with the same detector at different distances. In this case, the shape and normalization of the ν e spectrum as well as the detector efficiency are canceled out. The DANSS experiment uses this strategy and measures ν e spectra at 3 distances from the reactor core centre: 10.7 m, 11.7 m, and 12.7 m to the detector centre. The detector positions are changed typically 3 times a a e-mail: mark.shirchenko@jinr.ru b e-mail: nataliya.skrobova@gmail.com week. Antineutrinos are detected by means of the Inverse Beta Decay (IBD) reaction ν e + p → e + + n with E ν = E e + + 1.80 MeV. (2)

The DANSS detector
The DANSS detector was constructed by the ITEP-JINR collaboration. It is installed under the core of a 3.   Figure 2a shows the difference between the MC and data divided by the data for the main part of the n-Gd peak. There is a good agreement between the MC and data. On the other hand, the slight changes in the MC energy scale or in the MC energy resolution lead to serious discrepancies between the data and MC (see Fig. 2b and Fig. 2c). This comparison indicates the scale of the systematic uncertainties of these parameters. It is very difficult to simulate reliably the low energy part of the n-Gd capture signal since there are many cascade decay chains with unknown probabilities. Our MC does not describe well the lower energy part of the spectrum and hence we do not use it for the comparison. Figure 3 shows the energy distribution of signals from a 60 Co and 22 Na γsources placed in the center of the detector. The observed energy resolutions and peak positions are consistent with the MC expectations. The SiPM gain calibration was performed typically every 5 days with noise signals. Calibration with cosmic muons of all strips in the whole detector was also performed once in 5 days. A detailed description of the calibration procedure is presented in [15]. High granularity of the detector allows to reconstruct muons crossing the strips at different angles. Energy deposit inside the strip is proportional to the muon track length in the strip. The accuracy of track reconstruction algorithm was estimated by MC by comparing reconstructed and generated tracks. Figure 4 shows the deviation of the reconstructed length inside the strip from its generated value. The accuracy is better than 0.5%. After correcting for cross-talk and saturation curve, the strip response to the energy deposited by cosmic muons is linear within 0.7% in the range (1.7-4.7) MeV (  PMTs. The PMT linearity was also checked using the LED calibration system. Therefore, the PMT energy response is also linear. Positrons with energies higher than 4.7 MeV typically deposit their energy in several strips. Therefore, the detector response should be linear for high energies as well.

Data taking and analysis
The trigger of the experiment is produced when the digital sum of all PMT signals is above 0.7 MeV or the energy in the veto system is larger than 4 MeV. The IBD process appears in the data as two distinct events, prompt and delayed. For each trigger, waveforms for all SiPMs and PMTs are recorded in 512 ns windows. The visible energy of a positron cluster (continuous cluster of hits in the strips) is converted using MC simulations into the deposited energy by taking into account average losses in the inactive reflective layers of the strips and dead channels. Sometimes photons from the positron annihilation produce signals in the strips attributed to the positron cluster. This leads to an increase of the visible energy. Such a shift is also corrected on average using MC simulations. A typical size of the total correction is ∼2%. The next step is a search for the time-correlated pairs of prompt-delayed events. We start with searching for an event with more than 3.5 MeV energy deposit. This is a delayed event candidate unless it has the muon veto. Then we look backward in time searching for a prompt event with more than 1 MeV in the positron cluster and no muon veto. An IBD candidate pair is considered found if the time difference between the prompt and delayed events is in the range (2-50) µs. For a valid pair we also require no event with the muon veto within 60 µs before the prompt signal (within 200 µs if E > 300 MeV is released in the main detector). No other event should occur within 45 µs before and 80 µs after the prompt event.
The found pairs of prompt and delayed events form the experimental sample of IBD candidates. Similar to the experimental sample, the accidental coincidence sample is formed by looking for a prompt signal in 16 regions: 5, 10,..., 80 ms before the neutron candidate. This sample provides us with a model-independent measure of the accidental background. Distributions for IBD candidates, the accidental background and their difference, which represents the IBD signal without accidental background are presented in Fig. 6.
Several cuts are applied in order to reduce the accidental background. These cuts are designed to be very soft with respect to the signal in order to avoid any distortions. All cuts were selected without looking at the final results. They have been fixed after collection of about 10% of the data. The cuts include the following requirements: The energy spectrum of the background from neutrons produced by muons inside the veto system is obtained from events with the muon veto. The amount of this background is determined from a fit of the positron candidate energy spectrum during reactor off periods using the shape of the background determined from events with the muon veto. This procedure reduces uncertainties in the background shape to a negligible level. A possible small uncertainty in the background rate is taken into account during systematic error studies. This is the most important background. It constitutes 2.7% of the IBD rate at the top detector position. Rough estimates of the fast neutron penetration probability through the massive reactor shielding indicate that this background is much smaller than 0.1 events/day. In addition, fast neutrons should interact predominantly in the outer region of the detector. Such an increase is observed for neutrons produced by muons inside the detector shielding. On the other hand, no such increase is observed for the IBD candidates. Nevertheless to be safe, the outer 4 cm area of the detector in all 3 dimensions is not included into the data analysis.
The shape of the positron spectrum agrees roughly with the MC predictions based on the ν e spectrum from [3,16]. However, a quantitative comparison requires additional studies of calibration and systematic errors and improvements in the MC simulation of the detector. The shapes of the ν e spectra are different for 235 U and 239 Pu isotopes. The fractions of these isotopes change during a reactor campaign. The amount of 235 U decreases while the amount of 239 Pu increases with time. This leads to changes in the ν e spectrum first observed in [17]. Figure 8 shows the ratio of positron spectra collected during 3 months before the end of the reactor campaign and during the 2-4 months after beginning of the campaign. The corresponding fractions of 239 Pu fission fractions are 37.7% and 27.1% correspondingly. We do not have reliable information about the corresponding fraction during the first month after the start of the reactor campaign. The changes in the positron spectrum are obvious. They are well described by the MC expectations based on the ν e spectra from [3,16]. Figure 9 shows the correlation between the reactor thermal power and the number of registered IBD events. The two distributions were equalized during one month period in 2016. The number of IBD events was corrected for the fuel evolution using the model of the ν e spectra [3,16]. After that the IBD rate coincides with the reactor power with about 2% accuracy during 16 months. The only exception is the one month period after the latest beginning of the campaign for which we do not have reliable data on the isotope fractions. Figure 10 shows the ratio of positron energy spectra at the bottom and top detector positions. The exclusion area in the sterile neutrino parameter space was calculated using the Gaussian CL s method [18] assuming only one type of sterile neutrinos. For a grid of points in the m 2 14 , sin 2 2θ 14 plane predictions for the ratio R pre i of positron spectra at the bottom and top detector positions were calculated. Calculations included the MC integration over the ν e production point in the reactor core, ν e detection point in the detector, and positron energy resolution. The ν e production point distributions in the reactor core were provided by the KNPP for different time periods. The distribution averaged over the campaign was used in the calculations. It was checked that this approximation practically did not influence the final results. The obtained theoretical prediction for a given point in the m 2 14 , sin 2 2θ 14 plane was compared with the prediction for the three neutrino case using the Gaussian CL s method for the 90% confidence level (CL) exclusion area estimation. The difference in χ 2 for the two hypotheses χ 2 = χ 2 4ν − χ 2 3ν was used for the comparison. The χ 2 for each hypothesis was constructed using 24 data points R obs i in the (1−7) MeV positron energy range where R obs i (R pre i ) is the observed (predicted) ratio of ν e counting rates at the two detector positions and σ i is the statistical standard deviation of R obs i , and k is a normalization factor equal to the ratio of the total number of the IBD events per day at the bottom and top detector positions (MC events number were equal for different positions). The oscillations due to the known neutrinos were neglected since at such short distances they do not change the ν e spectrum. The procedure was repeated for all points of the grid in order to get the whole exclusion area. Influence of systematic uncertainties in the parameters was Figure 11. 90% (light cyan) and 95% (dark cyan) CL exclusion area in m 2 14 , sin 2 2θ 14 parameter space. The shaded area represents our analysis. Curves show allowed regions from neutrino disappearance experiments [4,21], and the star is the best point from the RAA and GA fit [4]. estimated by repeating the analysis with different values of parameters. A point in the m 2 14 , sin 2 2θ 14 plane was included into the final exclusion area if it appeared in the exclusion areas for all tested variations of the parameters. We varied the energy resolution, the background level and energy scale by 10%, 15% and 2% correspondingly. We also used a reduced energy range of (1.5−6) MeV in the fit. Figure 11 shows the obtained 90% and 95% CL excluded area in the m 2 14 , sin 2 2θ 14 plane. For some values of m 2 14 the obtained limits are more stringent than previous results [6,19,20]. It is important to stress that our results are based only on the comparison of the positron energy distributions at the two distances measured with the same detector. Therefore the results do not depend on the ν e spectrum shape and normalization as well as on the detector efficiency. The method used in our analysis is very insensitive to systematic errors since the influence of the errors is canceled out in the ratio of the positron spectra at the two distances. This is illustrated by Fig. 12. It shows that the excluded areas with and without the systematic errors differ very little. The excluded area covers a large fraction of regions indicated by the GA and RAA. In our analysis the point m 2 14 = 1.4eV 2 , sin 2 2θ 14 = 0.05 has the smallest χ 2 = 21.9. The difference in χ 2 with the 3ν case is 13.1. The significance of this indication of the existence of the sterile neutrino will be studied taking into account systematic uncertainties after collection of more data this year.